The statistically unbounded $\tau$-convergence on locally solid Riesz spaces

Özet

Öz A sequence xn in a locally solid Riesz space E, τ is said to be statistically unbounded τ -convergent to x ∈ E if, for every zero neighborhood U , 1 n {k ≤ n : |xk − x| ∧ u /∈ U} → 0 as n → ∞. In this paper, we introduce the concept of the st-uτ -convergence and give the notions of st-uτ -closed subset, st-uτ -Cauchy sequence, st-uτ -continuous and st-uτ -complete locally solid vector lattice. Also, we give some relations between the order convergence and the st-uτ -convergence.